The word sidereal comes from the latin for "star". A sidereal day is the time taken for the stars to appear in the same place in the night sky. This corresponds to one full rotation of the Earth (from 1-2 in the diagram on the right). A sidereal day is 23 hours 56 minutes and 4.09 seconds long.
The word synodic derives from the Greek word for meeting or assembly. A synodic, or solar day is the amount of time taken for the Sun to return to the observer's meridian. From the diagram above, we see that the Earth has to rotate a little more than 360° for the Sun to appear in the same place in the sky. A solar day is, on average, 24 hours long. Because the Earth's orbit is slightly elliptical, the length of any given solar day can be slightly different to 24 hours.